Resonant Interactions of Vector Breathers

We study vector solitons propagating on an unstable constant background (vector breathers) theoretically in the framework of the focusing two-component one-dimensional nonlinear Schrödinger equation. Based on the simplified inverse scattering transform technique called the dressing method, we find the exact solutions describing resonance interactions of the vector breathers. The resonance represents a three-breather process, i.e., a fusion of two breathers into one or decay of one breather into two, such that the characteristic wave vectors and frequencies of the breathers satisfy resonance conditions.